We determine the full statistics of nonstationary heat transfer in Kipnis-Marchioro-Presutti lattice gas model at long times by uncovering and exploiting complete integrability underlying equations macroscopic fluctuation theory. These are closely related to derivative nonlinear Schr\"odinger equation (DNLS), we solve them Zakharov-Shabat inverse scattering method (ISM) adapted D. J. Kaup A. C. Newell, Math. Phys. 19, 798 (1978) for DNLS. obtain explicit results exact large deviation...

We develop a first-principles approach to compute the counting statistics in ground state of $N$ noninteracting spinless fermions general potential arbitrary dimensions $d$ (central for $d>1$). In confining potential, Fermi gas is supported over bounded domain. $d=1$, specific potentials, this system related standard random matrix ensembles. study quantum fluctuations number ${\mathcal{N}}_{\mathcal{D}}$ domain $\mathcal{D}$ macroscopic size bulk support. show that variance grows as...

We study the full nonequilibrium steady-state distribution P_{st}(X) of position X a damped particle confined in harmonic trapping potential and experiencing active noise whose correlation time τ_{c} is assumed to be very short. Typical fluctuations are governed by Boltzmann with an effective temperature that found approximating as white Gaussian thermal noise. However, large deviations described non-Boltzmann distribution. find that, limit τ_{c}→0, they display scaling behavior...

Abstract We investigate non-stationary heat transfer in the Kipnis–Marchioro–Presutti (KMP) lattice gas model at long times one dimension when starting from a localized distribution. At large scales this initial condition can be described as delta-function, u ( x , t = 0) Wδ ). characterize process by transferred to right of specified point X time T <?CDATA $J={\int }_{X}^{\infty }u(x,t=T)\mathrm{d}x,$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"...

We study the short-time distribution P(H,L,t) of two-point two-time height difference H=h(L,t)-h(0,0) a stationary Kardar-Parisi-Zhang interface in 1+1 dimension. Employing optimal-fluctuation method, we develop an effective Landau theory for second-order dynamical phase transition found previously L=0 at critical value H=H_{c}. show that |H| and L play roles inverse temperature external magnetic field, respectively. In particular, find first-order when changes sign, supercritical H. also...

We study $N$ spinless fermions in their ground state confined by an external potential one dimension with long range interactions of the general Calogero-Sutherland type. For some choices this system maps to standard random matrix ensembles for values Dyson index $\beta$. In fermion model $\beta$ controls strength interaction, $\beta=2$ corresponding noninteracting case. quantum fluctuations number ${\cal N}_{\cal D}$ a domain $\cal{D}$ macroscopic size bulk Fermi gas. predict that variance...

We study the fluctuations of area $A(t)= \int_0^t x(\tau)\, d\tau$ under a self-similar Gaussian process (SGP) $x(\tau)$ with Hurst exponent $H>0$ (e.g., standard or fractional Brownian motion, random acceleration process) that stochastically resets to origin at rate $r$. Typical $A(t)$ scale as $\sim \sqrt{t}$ for large $t$ and on this distribution is Gaussian, one would expect from central limit theorem. Here our main focus atypically $A(t)$. In long-time $t\to\infty$, we find full takes...

Given a random process $x(\tau)$ which undergoes stochastic resetting at constant rate $r$ to position drawn from distribution ${\cal P}(x)$, we consider sequence of dynamical observables $A_1, \dots, A_n$ associated the intervals between events. We calculate exactly probabilities various events related this sequence: that last element is larger than all previous ones, monotonically increasing, etc. Remarkably, find these are ``super-universal'', i.e., they independent particular $x(\tau)$,...

This work reports the first experimental measurements of this distribution by tracking Brownian motion colloidal particles. Unexpected connections between Airy and large-deviation formalisms non-equilibrium statistical mechanics are found. Finally, a particle position distribution, conditioned on given area, is studied, two novel dynamical phase transitions uncovered.

The optimal fluctuation method—essentially geometrical optics—gives a deep insight into large deviations of Brownian motion. Here we illustrate this point by telling three short stories about motions, 'pushed' large-deviation regime constraints. In story 1 compute the short-time deviation function (LDF) winding angle particle wandering around reflecting disk in plane. Story 2 addresses stretched motion above absorbing obstacles We LDF position surviving at an intermediate point. 3 deals with...

We consider an overdamped run-and-tumble particle in two dimensions, with self-propulsion orientation that stochastically rotates by 90^{∘} at a constant rate, clockwise or counterclockwise equal probabilities. In addition, the is confined external harmonic potential of stiffness μ, and possibly diffuses. find exact time-dependent distribution P(x,y,t) particle's position, particular, steady-state P_{st}(x,y) reached long-time limit. also for "free" particle, μ=0. achieve this showing that,...

We study the ground state of $N\ensuremath{\gg}1$ noninteracting fermions in a two-dimensional harmonic trap rotating at angular frequency $\mathrm{\ensuremath{\Omega}}>0$. The support density Fermi gas is disk radius ${R}_{e}$. calculate variance number fermions, ${\mathcal{N}}_{R}$, inside $R$ centered origin for bulk gas. find rich and interesting behaviors two different scaling regimes, (i) $\mathrm{\ensuremath{\Omega}}/\ensuremath{\omega}<1$ (ii)...

Large deviations in chaotic dynamics have potentially significant and dramatic consequences. We study large of series finite lengths $N$ generated by maps. The distributions generally display an exponential decay with $N$, associated large-deviation (rate) functions. obtain the exact rate functions analytically for doubling, tent, logistic For latter two, solution is given as a power whose coefficients can be systematically calculated to any order. also function cat map numerically,...

We consider a system of $N$ noncrossing Brownian particles in one dimension. find the exact rate function that describes long-time large deviation statistics their occupation fraction finite interval space. Remarkably, we that, for any general $N\ensuremath{\ge}2$, undergoes $N\ensuremath{-}1$ dynamical phase transitions second order. The are boundaries phases correspond to different numbers which vicinity throughout dynamics. achieve this by mapping problem finding ground-state energy...

Abstract We calculate the steady state distribution <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>SSD</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="bold-italic">X</mml:mi> stretchy="false">)</mml:mo> </mml:math> of position a Brownian particle under an intermittent confining potential that switches on and off with constant rate γ . assume external <mml:mi>U</mml:mi>...

Established populations often exhibit oscillations in their sizes that, the deterministic theory, correspond to a limit cycle space of population sizes. If is isolated, intrinsic stochasticity elemental processes can ultimately bring it extinction. Here we study extinction oscillating stochastic version Rosenzweig-MacArthur predator-prey model. To this end develop WKB (Wentzel, Kramers and Brillouin) approximation master equation, employing characteristic size as large parameter. Similar...

We determine the exact short-time distribution $\ensuremath{-}ln{\mathcal{P}}_{\text{f}}\left(H,t\right)={S}_{\text{f}}\left(H\right)/\sqrt{t}$ of one-point height $H=h(x=0,t)$ an evolving $1+1$ Kardar-Parisi-Zhang (KPZ) interface for flat initial condition. This is achieved by combining (i) optimal fluctuation method, (ii) a time-reversal symmetry KPZ equation in dimension, and (iii) recently determined...

We consider an overdamped particle with a general physical mechanism that creates noisy active movement (e.g., run-and-tumble or Brownian particle, etc.), is confined by external potential. Focusing on the limit in which correlation time $\ensuremath{\tau}$ of noise small, we find nonequilibrium steady-state distribution ${P}_{\text{st}}(\mathbit{X})$ particle's position $\mathbit{X}$. While typical fluctuations $\mathbit{X}$ follow Boltzmann effective temperature not difficult to find,...

Confined active particles constitute simple, yet realistic, examples of systems that converge into a nonequilibrium steady state. We investigate run-and-tumble particle in one spatial dimension, trapped by an external potential, with given distribution $g(t)$ waiting times between tumbling events whose mean value is equal to $\ensuremath{\tau}$. Unless exponential (corresponding constant rate), the process non-Markovian, which makes analysis model particularly challenging. use analytical...

We investigate analytically the distribution tails of area $A$ and perimeter $L$ a convex hull for different types planar random walks. For $N$ noninteracting Brownian motions duration $T$ we find that large-$L$ -$A$ behave as $\mathcal{P}(L)\ensuremath{\sim}{e}^{\ensuremath{-}{b}_{N}{L}^{2}/DT}$ $\mathcal{P}(A)\ensuremath{\sim}{e}^{\ensuremath{-}{c}_{N}A/DT}$, while small-$L$ $\mathcal{P}(L)\ensuremath{\sim}{e}^{\ensuremath{-}{d}_{N}DT/{L}^{2}}$...

We study a Brownian excursion on the time interval $\left|t\right|\leq T$, conditioned to stay above moving wall $x_{0}\left(t\right)$ such that $x_0\left(-T\right)=x_0\left(T\right)=0$, and $x_{0}\left(\left|t\right|<T\right)>0$. For whole class of walls, typical fluctuations are described by Ferrari-Spohn (FS) distribution exhibit Kardar-Parisi-Zhang (KPZ) dynamic scaling exponents $1/3$ $2/3$. Here we use optimal fluctuation method (OFM) atypical fluctuations, which turn out be quite...

We investigate the statistics of local time T=∫_{0}^{T}δ(x(t))dt that a run and tumble particle (RTP) x(t) in one dimension spends at origin, with or without an external drift. By relating to number times RTP crosses we find distribution P(T) satisfies large deviation principle P(T)∼e^{-TI(T/T)} observation limit T→∞. Remarkably, presence drift rate function I(ρ) is nonanalytic: interpret its singularity as dynamical phase transition first order. then extend these results by studying amount...

We study the complete probability distribution of time-averaged height at point x = 0 an evolving 1 + dimensional Kardar–Parisi–Zhang (KPZ) interface . focus on short times and flat initial condition employ optimal fluctuation method to determine variance third cumulant distribution, as well asymmetric stretched-exponential tails. The tails scale , similarly previously determined one-point KPZ statistics specified time histories, dominating these tails, are markedly different. Remarkably,...